Brief Description of Analysis.

Two muons are selected using IsolatedLeptonTagging (without E_{\mathrm{yoke}} and impact parameters) as the H \to \mu ^+ \mu ^- candidate. Various pre-cuts are applied to select signal and reject background. Further background rejection is done using TMVA(BDTG). Estimating the precision on \sigma \times \mathrm{BR}(H \to \mu ^+ \mu ^-) is done using toy MC technique. In the signal process, two processes are mixed up: e^+ e^- \to ZH \to \nu \overline{\nu} \mu ^+ \mu ^- and e^+ e^- \to \nu \overline{\nu}H \to \nu \overline{\nu} \mu ^+ \mu ^- via WW-fusion. These two should be separated in the end, but such separation is not considered in the analysis; it is beyond the scope of this analysis.

Candidate Plots for IDR.

Some comparison between IDR-L and IDR-S in reconstructed particle level has done. More details can be found in my talk on 2019Apr03. All plots are left-handed beam polarization. All histograms are normalized to 1.

Only ~5% events are the case with both muons flying in endcap/forward region. We will not discuss here.

Remaining Events After All Cuts.

A toy MC technique is applied by using overall M_{\mu ^+ \mu ^-} distribution after BDTG score cut to estimate the precision on \sigma \times \mathrm{BR}(H \to \mu ^+ \mu ^-). Two detector models and two beam polarization cases are considered. Next table shows the total remaining events in the full range (120 - 130 GeV) after BDTG score cut for each detector model and each beam polarization.

IDR-L-left

IDR-S-left

IDR-L-right

IDR-S-right

N_{\mathrm{sig}}

33.17

33.01

5.43

5.26

N_{\mathrm{bkg}}

1101.55

1069.25

245.34

202.37

In the right-handed case, N_{\mathrm{sig}} is pretty small, hard to perform precise measurement. We only have ~8 signal events with 1600 fb-1 statistics from the beginning. We will not consider right-handed case for further discussion.

We see some differences in N_{\mathrm{bkg}} between IDR-L and IDR-S, but this is due to statistical fluctuation caused by the lack MC statistics for SM background.

Discussion and Final Results.

From the table above, N_{\mathrm{sig}} and N_{\mathrm{bkg}} in the full range are pretty much same between IDR-L and IDR-S. The level of total background fluctuates due to limited number of MC statistics, thus, we can conclude that the background distribution and total number of backgrounds in full range are the same. For further analysis, we treat the background condition is common in IDR-L and IDR-S. We take the average number of N_{\mathrm{bkg}} and average slope in background modeling of IDR-L and IDR-S, for generating pesudo-background data. We perform toy MC using common parametrization for background, and evaluate the precision. Next table shows the final result of the precision on \sigma \times \mathrm{BR}(H \to \mu ^+ \mu ^-) after 50000 times pseudo-experiments. The theoretical number is provided in addition which assumes 100% signal efficiency, no backgrounds, and no detector effects.

IDR-L

IDR-S

Theory

precision

40.16 \pm 0.15{\%}

41.28 \pm 0.15{\%}

13.18{\%}

My real analysis is about a factor of 3 worse than the theoretical number. There are several reasons mixed up: imperfection of cuts, existence of irreducible backgrounds mainly come from e^+ e^- \to W^+ W^- \to 2\mu 2\nu, detector effect, and so on.

IDR-L gives relatively 2.8% better precision than IDR-S.

Because overall M_{\mu ^+ \mu ^-} distribution is better in IDR-L. In detail, IDR-L gives significantly better performance in "barrel category", and similar performance in "mixed category". Almost all events are categorized in these two groups, resulting better result with IDR-L.

The number of signal events in M_{\mu ^+ \mu ^-} peak region is basically same between IDR-L and IDR-S, but ~10% more backgrounds lyng in the peak region with IDR-S due to ~10% wider width caused by worse momentum resolution. This ~10% more backgrounds can translate into ~3.3% difference in the statistical significance. This 2.8% difference is consistent to the estimation from statistics.

Conclusion.

IDR-L gives better result than IDR-S, because of better momentum resolution in barrel region.